WO2017076036A1

WO2017076036A1 - Shifted sub-carrier-based frequency domain chaotic cognitive radio system

Info

Publication number: WO2017076036A1
Application number: PCT/CN2016/088632
Authority: WO
Inventors: 卢怀因; 张琳
Original assignee: 中山大学
Priority date: 2015-11-02
Filing date: 2016-07-05
Publication date: 2017-05-11
Also published as: CN105429747A

Abstract

The invention discloses a shifted sub-carrier-based frequency domain chaotic cognitive radio system comprising a transmitter and a receiver. At the transmitter, a frequency domain chaotic signal generator is configured to generate a frequency domain-based chaotic signal c(t), a sub-carrier correspondence module is configured to dynamically change a corresponding relationship between a chaotic sequence C(k) and a sub-carrier, data information undergoes a binary phase shift keying modulation to provide b(t), b(t) and c(t) are modulated together to provide s(t), and s(t) is further modulated with a carrier and transmitted over a radio channel in an available frequency band. At the receiver, after coherent carrier demodulation, a frequency domain chaotic signal generator is configured to generate a frequency domain-based chaotic signal c(t), the chaotic signal c(t) is then synchronized and used to demodulate a receiving signal r(t) to obtain d(t), a zero-crossing determination is performed on d(t) to obtain an estimate b̑(t) of an information bit, thereby successfully receiving the transmitted information. The shifted sub-carrier-based frequency domain chaotic cognitive radio system disclosed by the invention significantly improves security of a conventional frequency domain chaotic cognitive radio system.

Description

A frequency domain chaotic cognitive radio system based on subcarrier shift

Technical field

The invention is oriented to the field of wireless communication, and proposes a frequency domain chaotic cognitive radio system based on subcarrier shifting, which transmits information through a randomly generated chaotic sequence-subcarrier pair, and improves the security characteristics of the cognitive radio system.

Background technique

Spectrum congestion is a bottleneck affecting the performance of wireless communication systems. Cognitive radio technology can detect the available frequency bands and thus access in non-continuous frequency holes to make more bandwidth for signal transmission.

However, the cognitive radio communication system is the same as other wireless communication systems. Since the wireless channel is a broadcast channel, information is easily intercepted by eavesdropping users or malicious attackers, and the secure transmission of information is threatened and cannot be guaranteed.

In order to improve the security of cognitive radio systems, it has been proposed in the literature to apply chaotic processing technology to cognitive radio systems to form a high frequency spectrum utilization and high frequency spectrum utilization and frequency domain chaos recognition. Know the radio system.

The structure of the frequency domain chaotic cognitive radio system is shown in Fig. 1. At the transmitting end, the chaotic signal c(t) based on the frequency domain is generated by the frequency domain chaotic signal generator. The data information is modulated by BPSK (Binary Phase Shift Keying) to obtain b(t), which is modulated by c(t) and then transmitted by carrier modulation to the wireless channel of the available frequency band. At the receiving end, after the carrier coherent demodulation, the chaotic signal c(t) is generated in the same process as the transmitting end, and the chaotic signal is demodulated after the synchronization to obtain the d(t), and then the d (t) A zero-crossing decision is made to obtain b(i), and the transmitted information is successfully received.

The specific structure of the frequency domain multi-subcarrier chaotic signal generator is shown in Figure 2. Combined with the spectrum diagram obtained by the cognitive radio system to detect the surrounding radio environment, the chaotic sequence C(k) has passed through multiple orthogonal OFDM (Orthogonal Frequency Division). Multiplexing) Subcarrier modulation. The chaotic signal c(t) is generated after adding the cyclic prefix, string/parallel conversion and passing through the low pass filter.

The following first-order Logistic Map chaotic sequence generator can be used to generate a chaotic sequence, thereby generating a chaotic signal c(t):

C(k)=4C(k-1)-4C ² (k-1) k=1,2,...,C(k)∈(0,1) (1)

Although the above-mentioned frequency domain chaotic processing cognitive radio system improves the security performance of the system, the information interceptor is easy to learn the chaotic sequence generator and calculate the initial value of the chaotic sequence, thereby regenerating the chaotic sequence. Therefore, the existing frequency domain Chaotic processing cognitive radio systems are still difficult to meet the high security application requirements.

Summary of the invention

The present invention is directed to overcoming at least one of the above-mentioned problems (deficiencies) of the prior art. The present invention aims to improve the security of a communication system by physical layers, and combines subcarrier interleaving techniques and dynamic iteration of chaotic sequences to propose a subcarrier-based shift. The frequency domain chaotic cognitive radio system effectively protects the attacker from attacks by reconstructing chaos and improves the security of the frequency domain chaotic cognitive radio system.

In order to solve the above technical problem, the technical solution of the present invention is as follows:

A frequency domain chaotic cognitive radio system based on subcarrier shifting includes a transmitting end and a receiving end. At the transmitting end, a chaotic sequence C(k) is first generated by a chaotic sequence generator, and then a chaotic sequence C is implemented by a subcarrier corresponding module. (k) The dynamic relationship between the subcarrier and the subcarrier is dynamically changed, and the chaotic signal c(t) based on the frequency domain is generated by the frequency domain chaotic signal generator, and the input data information is BPSK modulated to obtain b(t), b(t) is c( t) modulated into s(t), and then transmitted by carrier modulation to the wireless channel of the available frequency band; at the receiving end, after the carrier coherent demodulation, the chaotic signal c(t) based on the frequency domain is also generated by the frequency domain chaotic signal generator. The chaotic signal c(t) demodulates the received signal r(t) after synchronization to obtain d(t), and then performs a zero-crossing decision on d(t) to obtain an estimated value of the information bits.

Successfully received the message sent.

Preferably, the specific manner in which the subcarrier corresponding module dynamically changes the correspondence between the chaotic sequence C(k) and the subcarrier is:

The subcarrier shifter dynamically pairs and modulates the chaotic sequence C(k) with the subcarrier, and the pairing relationship is jointly determined by the subcarrier shifter and the band map;

Among them, the spectrum map is obtained by the cognitive radio system sensing the spectrum usage of the surrounding spectrum conditions:

a(k) maps the input C(k). When the kth subcarrier is occupied, its frequency a(k) is set to 0. When the kth subcarrier is idle, its frequency a(k) is set to 1.

The signal after the IFFT is only included in the idle frequency component. After the spectrum usage information is obtained, the idle subcarrier is dynamically shifted according to the frequency band map according to the period T _SS . After the shift, a chaotic sequence of a specific arrangement is obtained. The sequence C(k) and the formulas (3)-(6), after generating the chaotic signal c(t) based on the frequency domain, modulate the communication information b(t), so that it is difficult for the eavesdropper to crack the communication system to obtain the communication information, and the dynamic Shift rule is represented as a shift matrix

Is a matrix of N _NC × N _NC , where N _NC is the number of available subcarriers detected by the cognitive radio system, k = 1, 2, ..., N _NC ; shift matrix

Determined by a chaotic sequence C _M (k) of dimension N _NC ×1, the former C(k) is used for OFDM modulation, and finally the input chaotic sequence of c(t) is generated, and C _M (k) is used for Generating a shift matrix

The chaotic sequences, which are all generated by equation (1), are only iterated by different initial values C(1). With the dynamic iteration of C _M (k),

The matrix changes dynamically;

Said

There is only one non-zero element "1" in each row and each column. By sorting the chaotic sequence C _M (k) from small to large, the sorted chaotic sequence C _MSort (k) is obtained by C _M (k) and C _MSort (k) generation

And

Is a matrix that transforms C _M (k) into C _MSort (k) with the transformation expression:

Available from (3):

In (4),

The function f _s (●) is defined as:

The elements of the i-th row and the j-th column of the above B _i,j matrix B, A represents a random matrix, which is used to describe the definition of f _s (●), and A _i,j represents the i-th row and the j-th column of the matrix A. Elements;

Since the chaotic sequence C _M (k) can be dynamically iterated by the chaotic sequence generator, it changes once every certain time.

It also changes dynamically, making it difficult for an attacker to obtain the subcarrier shifting law, which significantly enhances the security of the transmitted data.

After the dynamic shifting process, the OFDM subcarrier modulation is performed on the chaotic sequence; after adding the cyclic prefix, the serial/parallel conversion and passing through the low pass filter, a chaotic signal c(t) is generated;

Where N is the total length of the chaotic sequence, C(k) is the chaotic sequence of the kth term generated by the chaotic sequence generator; kΔf is the kth subcarrier, where

T _S is the symbol period of OFDM; p(t) is a unit height rectangular wave having a width of one symbol period.

Preferably, in the frequency domain chaotic cognitive radio system based on subcarrier shift, BPSK is used to modulate the binary bit b(t) of the input system, and multiplied by the OFDM modulated chaotic signal c(t) to obtain s ( t), s(t) is expressed as:

After being modulated by the carrier cos(2πf _c t), the signal is transmitted to the AWGN channel;

At the receiving end, the signal expression at time t is received:

r(t)=s(t)+n(t) (10)

Where n(t) is a mean of 0 and the variance is

The AWGN noise signal is demodulated at the receiving end by the same process as the transmitting end to generate c(t), r(t) and c ^* (t) to obtain d(t):

d(t)=r(t)c ^* (t)=b(t)|c(t)| ^* +n(t)c ^* (t) (11)

Then a zero-crossing decision on d(t) yields an estimate of the information bits.

Complete the communication process.

Compared with the prior art, the technical solution of the present invention has the beneficial effects that the present invention combines a subcarrier interleaving technique and a dynamic iterative generating process of a chaotic sequence, and proposes a frequency domain chaotic cognitive radio system based on subcarrier shifting. In this system, a user transmits information through a chaotic subcarrier pair, which is obtained by combining a chaotic sequence with an idle available subcarrier detected by a cognitive radio system. The correspondence between chaotic sequences and available subcarriers is dynamically shifted according to the shift period. The shift rule is defined by a chaotic sequence generated by another chaotic sequence generator. Thus, as the chaotic sequence is dynamically iterated, the shift is performed. The dynamic change of the bit rule effectively prevents the attacker from obtaining the shift rule. From the theoretical analysis and simulation results, the frequency domain chaotic cognitive radio system based on subcarrier shift proposed by the present invention can significantly improve the security of the original frequency domain chaotic cognitive radio system.

DRAWINGS

FIG. 1 is a schematic structural diagram of a frequency domain chaotic cognitive radio system.

2 is a schematic structural diagram of a frequency domain multi-subcarrier chaotic signal generator.

3 is a schematic diagram of a frequency domain chaotic cognitive radio system based on subcarrier shifting.

4 is a schematic structural diagram of a frequency domain chaotic signal generator and a subcarrier corresponding module.

FIG. 5 is an exemplary diagram of a subcarrier shifter.

Figure 6 is a graph of system performance.

detailed description

The drawings are for illustrative purposes only and are not to be construed as limiting the scope of the invention; some of the components of the drawings may be omitted, enlarged or reduced, and do not represent the dimensions of the actual product;

It will be apparent to those skilled in the art that certain known structures and their description may be omitted. The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

The present invention utilizes subcarrier shifting techniques to improve the security of a frequency domain chaotic cognitive radio system. Combined with subcarrier shifting technique and frequency domain chaotic cognitive radio system, the structure of frequency domain chaotic cognitive radio system based on subcarrier shift can be obtained as shown in Fig. 3. Compared with the frequency domain chaotic cognitive radio system in FIG. 1 , the difference is that in the system of FIG. 3 , a subcarrier dynamic shift module, that is, a “subcarrier corresponding module” in the figure is implemented, and the subcarrier is implemented. - Dynamic change of chaotic sequence pairs to improve the security of information transmission.

system structure

As shown in FIG. 3, at the transmitting end, the frequency domain chaotic signal generator generates a chaotic signal c(t) based on the frequency domain, and the subcarrier corresponding module dynamically changes the correspondence relationship between the chaotic sequence C(k) and the subcarrier. The data information is BPSK modulated to obtain b(t), which is modulated by c(t) and then transmitted by carrier modulation to the wireless channel of the available frequency band. At the receiving end, after the carrier coherent demodulation, the chaotic signal c(t) is generated in the same process as the transmitting end, and the chaotic signal is demodulated after the synchronization to obtain the d(t), and then the d (t) A zero-crossing decision is made to obtain b(i), and the transmitted information is successfully received.

Frequency domain chaotic signal generator and subcarrier corresponding module

4 is a structural diagram of a frequency domain chaotic signal generator and a subcarrier corresponding module, and a chaotic sequence C(k) corresponding to the dynamically shifted subcarrier is generated by a chaotic sequence generator corresponding to the formula (1).

C(k)=4C(k-1)-4C ² (k-1) k=1,2,...,C(k)∈(0,1) (1)

Different from the fixed chaotic sequence and subcarrier correspondence in FIG. 2, the subcarrier shifter in FIG. 4 dynamically pairs and modulates the chaotic sequence C(k) with the subcarrier, and the pairing relationship is performed by the subcarrier shifter and The band map is determined together. Among them, the spectrum map is obtained by the cognitive radio system sensing the spectrum usage of the surrounding spectrum conditions:

After obtaining the spectrum information, the idle subcarrier is dynamically shifted by the period T _SS according to the frequency band map, and the shift rule can be expressed as a shift matrix.

Is a matrix of N _NC × N _NC , where N _NC is the number of usable subcarriers detected by the cognitive radio system, the matrix is determined by a chaotic sequence C _M (k) of dimension N _NC ×1, with Dynamic iteration of C _M (k),

The matrix changes dynamically. In the actual communication process, the attacker needs to try to find the correspondence between the correct chaotic sequence and the subcarrier.

All possibilities, this complexity is O(N _NC !). FIG. 5 is an example of a subcarrier shifter.

Subcarrier shifter

Is a transformation matrix, so

Each row and column has only one non-zero element "1". By sorting the chaotic sequence C _M (k) from small to large, we can get the sorted chaotic sequence C _MSort (k), which can be generated by C _M (k) and C _MSort (k).

Simultaneously

Available from (3):

In (4),

The function f _s (●) is defined as:

In Fig. 5, N _NC = 4, C _M = [0.10, 0.98, -0.92, -0.69] ^T , and C _{M is} arranged from small to large, and C _MSort = [-0.92, -0.69, 0.10, 0.98] can be obtained. ^T , where (●) ^T represents the transpose of the matrix. Combining (4) and (5), a shift matrix M ₄ can be generated:

M ₄ then chaotic sequence C (k) is displaced. In the present embodiment, C = [c ₁ , c ₂ , c ₃ , c ₄ ] ^T , which can be obtained:

C _S,1 =M ₄ C=[c3,c4,c1,c2] ^T (7)

Since C _M (k) can be dynamically iterated by equation (1), it changes once every certain time.

After the subcarrier shifter, the OFDM subcarrier modulation is performed on the chaotic sequence. The chaotic signal c(t) is generated after adding the cyclic prefix, string/parallel conversion and passing through the low pass filter.

Where N represents the total length of the chaotic sequence, C(k) represents the chaotic sequence of the kth term generated by the chaotic sequence generator; kΔf represents the kth subcarrier, where

Frequency domain chaotic cognitive radio system transceiver

In a frequency domain chaotic cognitive radio system based on subcarrier shift, BPSK is used to modulate the binary bit b(t) of the input system, and multiplied by the OFDM modulated chaotic signal c(t) to obtain s(t), s(t) can be expressed as:

After modulation by the carrier cos (2πf _c t), the signal is sent to the AWGN (Additive White Gaussian Noise) channel.

At the receiving end, the signal expression at time t is received:

r(t)=s(t)+n(t) (10)

Where n(t) is a mean of 0 and the variance is

AWGN noise signal. At the receiving end, c(t) is generated by the same process, and r(t) and c ^* (t) are demodulated to obtain d(t):

d(t)=r(t)c ^* (t)=b(t)|c(t)| ^* +n(t)c ^* (t) (11)

Complete the communication process.

Performance analysis

It can be known from the foregoing that dynamically changing the correspondence between the chaotic sequence and the subcarriers can be realized by shifting the chaotic sequence C(k) in addition to shifting the subcarriers as shown in FIG. 5. In order to facilitate the mathematical expression, the chaotic sequence is shifted. In Figure 4, assume

available:

From Fig. 4 and Fig. 5, c _S (t) is obtained by C _S (k) through the IFFT (Inverse Fast Fourier Transform) process, so

among them

Is the energy normalization factor,

Is a discrete Fourier transform matrix (DFT) with a dimension of N _NC × N _NC .

Assuming that the chaotic sequence can be fully synchronized, the energy of each chaotic bit is expressed as E _b , then the received signal-to-noise ratio (SNR) of each bit is

Where E _b can be obtained by the following expression:

Where (g) ^H is Hermitian Transpose,

It is the shift matrix of the transmitting end, and X is the shifting matrix of the receiving end. From formula (14):

among them

Is a unit matrix with dimensions N _NC . Based on equation (17), equation (16) can be reduced to:

Where E(g) is the mathematical expectation operator. Combining the conditional bit error rate (BER) formula of (18) and BPSK systems, assuming that the binary data is evenly distributed, the BER expression of the frequency domain chaotic cognitive radio system based on subcarrier shift in the AWGN channel can be obtained. formula:

Where Q(·) is a Gaussian Q function,

Since the legitimate user has a shift matrix

Information, so at the legitimate user receiving end, in equation (19)

The BER expression of the frequency domain chaotic cognitive radio system based on subcarrier shift in the normal scenario can be obtained:

Next, the information leakage analysis of the frequency domain chaotic cognitive radio system based on subcarrier shift is performed. Assuming a probability distribution of 0 and 1 in the transmitted data, the mutual information between the transmitting data X transmitted by the transmitting end and the data Y _E recovered by the attacker at the receiving end is:

I _k (Y _E ;X)=H _k (Y _E )-H _k (Y _E X _E )=1+p _k log ₂ p _k +(1-p _k )log ₂ (1-p _k ) (21 )

Where H(g) is the information entropy operator and p _k is the BER of the attacker's receiver obtained by (19). Assuming that the N _NC subcarriers in the frequency domain chaotic cognitive radio system based on subcarrier shift are independent, the information leakage of the system can be expressed as:

In order to verify the performance of the frequency domain chaotic cognitive radio system based on subcarrier shift, we simulated the communication process of the system. In the simulation, communication simulation can be performed on the AWGN channel with the number of idle subcarriers N _NC = {16, 64, 256}. FIG. 6 is a graph showing the performance of the BER and information leakage as a function of SNR for a frequency domain chaotic cognitive radio system based on subcarrier shift proposed by the present invention.

Figure 6 is a graph of system performance, (a) BER performance curve, and (b) information leakage performance curve at the eavesdropper's receiving end.

Since the legitimate user knows all the key parameters used at the transmitter, the legal user's BER expression is (20). It can be obtained from Fig. 6(a) that the legal user theoretical curve and the simulation curve are coincident. As the number of available subcarriers increases, there is no significant change in BER performance, and "H.Li, X. Wang, and Y.Zou, "Dynamic Subcarrier Coordinate Interleaving for Eavesdropping Prevention in OFDM Systems," IEEE Commun. Lett., vol .18, pp.1059–1062, Jun.2014.” The BER performance deteriorates due to the channel estimation error due to the increase in the number of communication subcarriers, and “H.Li, X.Wang, and Y.Zou,” Dynamic Subcarrier Coordinate Interleaving for Eavesdropping Prevention in OFDM Systems, "IEEE Commun. Lett., vol. 18, pp. 1059–1062, Jun. 2014." Frequency Domain Chaos Cognition Based on Subcarrier Shift The radio system provides more stable normal communication. The BER of the eavesdropper is significantly higher than that of the legitimate user, and as the number of available subcarriers increases, the BER will gradually increase.

This phenomenon is caused by

The value is different from E[C ² (k)], and the signal demodulated by the detector at the receiver of the eavesdropper is destroyed, making it difficult to make a correct decision. For example, the E[C ² (k)] of the chaotic sequence generated by the chaotic sequence generator given by equation (1)

When the difference is 0.48 and 0.024, the difference is very obvious. Substituting into equations (19) and (20) respectively can yield a disparate BER performance curve, which is consistent with the simulation results in Fig. 6. Since the error rate is too high when recovering information, the eavesdropper will not be able to obtain the information transmitted in the system unless the correct shift matrix information is obtained.

It is assumed that the eavesdropper knows all the key system information except the correspondence between chaotic sequences and subcarriers, using equation (22), frequency domain chaotic cognitive radio system based on subcarrier shift and traditional frequency domain chaotic cognitive radio system. The information leakage at the receiving end of the eavesdropper is simulated, and Figure 6(b) is the simulation result. It can be seen from Fig. 6(b) that under this assumption, the frequency domain chaotic cognitive radio system based on subcarrier shift can significantly reduce the information leakage of the eavesdropper receiving end, while the traditional system has obvious information leakage.

It is apparent that the above-described embodiments of the present invention are merely illustrative of the present invention and are not intended to limit the embodiments of the present invention. Other variations or modifications of the various forms may be made by those skilled in the art in light of the above description. There is no need and no way to exhaust all of the implementations. Any modifications, equivalent substitutions and improvements made within the spirit and scope of the invention are intended to be included within the scope of the appended claims.

Claims

A frequency domain chaotic cognitive radio system based on subcarrier shifting, comprising a transmitting end and a receiving end, wherein at the transmitting end, a chaotic sequence C(k) is first generated by a chaotic sequence generator, and then a subcarrier corresponding module is generated. The dynamic relationship between the chaotic sequence C(k) and the subcarrier is dynamically changed, and the chaotic signal c(t) based on the frequency domain is generated by the frequency domain chaotic signal generator, and the input data information is BPSK modulated to obtain b(t), b(t). ) is modulated by c(t) into s(t), and then transmitted by carrier modulation to the wireless channel of the available frequency band; at the receiving end, after carrier coherent demodulation, frequency domain-based chaos is also generated by the frequency domain chaotic signal generator. The signal c(t), the chaotic signal c(t) demodulates the received signal r(t) after synchronization to obtain d(t), and then performs a zero-crossing decision on d(t) to obtain an estimated value of the information bit.
Successfully received the message sent.
The sub-carrier shift-based frequency domain chaotic cognitive radio system according to claim 1, wherein the specific method for dynamically changing the correspondence between the chaotic sequence C(k) and the subcarrier by the subcarrier corresponding module is:

The subcarrier shifter dynamically pairs and modulates the chaotic sequence C(k) with the subcarrier, and the pairing relationship is jointly determined by the subcarrier shifter and the band map;

Among them, the spectrum map is obtained by the cognitive radio system sensing the spectrum usage of the surrounding spectrum conditions:

a(k) maps the input C(k). When the kth subcarrier is occupied, its frequency a(k) is set to 0. When the kth subcarrier is idle, its frequency a(k) is set to 1.

The signal after the IFFT is only included in the idle frequency component. After the spectrum usage information is obtained, the idle subcarrier is dynamically shifted according to the frequency band map according to the period T SS . After the shift, a chaotic sequence of a specific arrangement is obtained. The sequence C(k) and the formulas (3)-(6), after generating the chaotic signal c(t) based on the frequency domain, modulate the communication information b(t), so that it is difficult for the eavesdropper to crack the communication system to obtain the communication information, and the dynamic Shift rule is represented as a shift matrix
Is a matrix of N NC × N NC , where N NC is the number of available subcarriers detected by the cognitive radio system, k = 1, 2, ..., N NC ; shift matrix
Determined by a chaotic sequence C M (k) of dimension N NC ×1, with the dynamic iteration of C M (k),
The matrix changes dynamically;

Said
There is only one non-zero element "1" in each row and each column. By sorting the chaotic sequence C M (k) from small to large, the sorted chaotic sequence C MSort (k) is obtained by C M (k) and C MSort (k) generation
And
Is a matrix that transforms C M (k) into C MSort (k) with the transformation expression:

Available from (3):

In (4),
The function f S (·) is defined as:

The elements of the i-th row and the j-th column of the above B i,j matrix B, A represents a random matrix, here is used to describe the definition of f S (·), and A i,j represents the i-th row and the j-th column of the matrix A. Elements;

Since the chaotic sequence C M (k) can be dynamically iterated by the chaotic sequence generator, it changes once every certain time.
It also changes dynamically, making it difficult for an attacker to obtain the subcarrier shifting law, which significantly enhances the security of the transmitted data.

After the dynamic shifting process, the OFDM subcarrier modulation is performed on the chaotic sequence; after adding the cyclic prefix, the serial/parallel conversion and passing through the low pass filter, a chaotic signal c(t) is generated;

Where N represents the total length of the chaotic sequence, C(k) represents the chaotic sequence of the kth term generated by the chaotic sequence generator; kΔf represents the kth subcarrier, where
T S is the symbol period of OFDM; p(t) is a unit height rectangular wave having a width of one symbol period.
The subcarrier shift based frequency domain chaotic cognitive radio system according to claim 2, wherein

In a frequency domain chaotic cognitive radio system based on subcarrier shift, BPSK is used to modulate the binary bit b(t) of the input system, and multiplied by the OFDM modulated chaotic signal c(t) to obtain s(t), s(t) is expressed as:

After being modulated by the carrier cos(2πf c t), the signal is transmitted to the AWGN channel;

At the receiving end, the signal expression at time t is received:

r(t)=s(t)+n(t) (10)

Where n(t) is a mean of 0 and the variance is
The AWGN noise signal is demodulated at the receiving end by the same process as the transmitting end to generate c(t), r(t) and c * (t) to obtain d(t):

d(t)=r(t)c * (t)=b(t)|c(t)| * +n(t)c * (t) (11)

Then a zero-crossing decision on d(t) yields an estimate of the information bits.
Complete the communication process.